Regenerative Braking Controller for Electric Motors

ABSTRACT

A method of regenerative braking includes providing an electric motor including at least one stator and a rotor, a speed of the rotor, a motor controller that regulates a current level in the stator winding, a power inverter which controls an energy flow to the stator terminal, and an energy storage system (ESS) which exchanges energy with the motor. A battery management circuit is between the power inverter and the ESS, and a processor has an associated memory storing a regenerative braking (RB) algorithm. The RB algorithm during braking causes the motor controller to execute determining an RB torque value from the rotor speed that maximizes regenerative braking current, and the power inverter is used to redirect the RB current to maximize a power transfer from the motor to the ESS.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This continuation application claims priority to U.S. patent applicationSer. No. 15/680,261, filed Aug. 18, 2017, which claims priority to U.S.patent application Ser. No. 14/837,810, filed Aug. 27, 2015, now U.S.Pat. No. 9,783,063, all of which are hereby incorporated herein byreference in their entirety.

FIELD

Disclosed embodiments relate to regenerative braking control forelectric motors.

BACKGROUND

An electric motor is a machine that converts electrical energy intomechanical energy. Electric motors include DC motors and AC motors. Onetype of AC motor is an AC induction motor. An AC induction motor istypically driven by 3-phase alternating current provided by an electricmotor controller coupled to a 3-phase inverter. The AC motor includes anoutside stationary stator having coils supplied with alternating currentto produce a rotating magnetic field, which induces a current in therotor windings. As the current flows through the rotor windings, asecond magnetic field is generated which interacts with the magneticfield from the stator to produce motion. The rotor is attached to theoutput shaft that is given a torque by the rotating magnetic field. Theinteraction of the rotor field and the stator field causes rotation ofthe rotor which can be used to perform work.

Another type of AC motor is a permanent magnet motor (PMM). PMMs havepermanent magnets located on the rotor and copper windings located onthe stator. The alternating current in the stator windings produces arotating magnetic field which interacts with the magnetic field from therotor magnets to produce motion. The frequency at which the statorcurrent oscillates determines the rotor's angular velocity and theresulting angular position.

Electric motors have two mechanical operations, motoring and braking. Ina torque vs. speed plot, quadrants I and III of the torque-speed planerepresent forward and reverse motoring operations and quadrants II andIV represent forward and reverse braking operations. The brakingoperation is regenerative when the electric motor is operated as anelectric generator such that the kinetic energy of the rotor isconverted to electricity and fed back to the power source. Not alloperating points in the braking quadrants are regenerative in nature,therefore, regenerative braking is a subset of the braking quadrants.The boundaries of the regenerative braking operation in the brakingquadrants need to be determined so that a closed-loop control systemdoes not place an operating point in the non-regenerative braking zonewhich causes the machine to draw power from the source in order toachieve braking.

SUMMARY

This Summary is provided to introduce a brief selection of disclosedconcepts in a simplified form that are further described below in theDetailed Description including the drawings provided. This Summary isnot intended to limit the claimed subject matter's scope.

Disclosed embodiments recognize braking an electric motor can removekinetic energy from the motor system if done properly, but inconventional electrical braking systems, this kinetic energy istypically not recovered by the system. During a typical electricalbraking process, additional electrical energy from the battery is neededto slow down the motor and none of the available kinetic energy isrecovered. Disclosed embodiments include an optimal regenerative braking(RB) algorithm which provides a braking torque for electric motors whichrecovers a significant amount of the kinetic energy when braking fromone speed to a lower speed.

Disclosed RB algorithms are independent of reference frametransformations and the method of motor control. The electric motoritself is controlled through disclosed software code which functions asthe brake so that there is no need for an external mechanical brake(such as hydraulic brakes in an automobile). Disclosed RB algorithmsalso apply to motor systems having an external mechanical brake. In thepresence of an external mechanical brake, disclosed RB algorithms can beused to make sure that the electric motor follows a prescribed torquetrajectory such that maximum current is returned to the energy storagesystem (ESS, such as a battery) during the braking event. Sincedisclosed RB algorithms are independent of reference frametransformations and the control method, the control scheme utilized withdisclosed algorithms can in one particular embodiment be field orientedcontrol (FOC). Disclosed RB algorithms can also be operated in astationary reference frame which removes the need for FOC.

For example, control schemes that can be used include the motorcontroller operating in the α/β frame, where the voltage/current in eachcoordinate is independently controlled and then transformed via aSpace-Vector Generator (SVG). This converts the desired voltage vector(Vαβ) into pulse width modulation (PWM) time durations to generate motorphase voltages (Vabc) or currents Iabc to provide the desired voltage orcurrent level. The motor controller can also operate in the A/B/C frameto allow control of the voltage/current of each of the motor phasesdirectly.

BRIEF DESCRIPTION OF THE DRAWINGS

Reference will now be made to the accompanying drawings, which are notnecessarily drawn to scale, wherein:

FIG. 1A depicts a torque vs. speed plot showing representative desiredand regenerative braking torques at a nominal rotor speed, according toan example embodiment.

FIG. 1B depicts a flow chart of the logic for an example RB strategy,according to an example embodiment.

FIG. 2A is a block diagram depiction of a controlled motor systemwithout an external brake within a common FOC controller, according toan example embodiment.

FIG. 2B is a block diagram depiction of a controlled motor systemincluding an external brake and an RB controller within a common FOCcontroller, according to an example embodiment.

FIG. 3 is a block diagram depiction of an example microcontroller unit(MCU) chip formed on a substrate implementing the FOC controller shownin FIG. 2B including the RB controller, external brake controller andbattery management circuit, according to an example embodiment.

FIG. 4 shows steps in an example method of RB where each torque vs.speed value generated is designed to maximize the RB current returned tothe ESS, according to an example embodiment.

FIG. 5 shows a simulated speed response for the case with disclosed RBalgorithm disabled.

FIG. 6 shows a simulated braking trajectory in the torque-speed planewith a disclosed RB algorithm disabled, according to an exampleembodiment.

FIG. 7 shows the simulated speed response with the disclosed RBalgorithm enabled.

FIG. 8 shows the simulated braking trajectory on the torque-speed planewith the disclosed RB algorithm enabled.

FIG. 9 shows the measured speed response with disclosed RB controldisabled.

FIG. 10 shows the measured speed response with disclosed RB controlenabled.

DETAILED DESCRIPTION

Example embodiments are described with reference to the drawings,wherein like reference numerals are used to designate similar orequivalent elements. Illustrated ordering of acts or events should notbe considered as limiting, as some acts or events may occur in differentorder and/or concurrently with other acts or events. Furthermore, someillustrated acts or events may not be required to implement amethodology in accordance with this disclosure.

Also, the terms “coupled to” or “couples with” (and the like) as usedherein without further qualification are intended to describe either anindirect or direct electrical connection. Thus, if a first device“couples” to a second device, that connection can be through a directelectrical connection where there are only parasitics in the pathway, orthrough an indirect electrical connection via intervening itemsincluding other devices and connections. For indirect coupling, theintervening item generally does not modify the information of a signalbut may adjust its current level, voltage level, and/or power level.

Disclosed methods of RB comprise providing an electric motor (motor)comprising a rotor, a measured or estimated speed of the rotor (rotorspeed) and braking torque values as a function of rotor speed, whereeach torque value is designed to maximize the RB current returned to theESS that is typically a battery. The general trend is that as the rotorspeed decreases, the level of braking torque decreases. A procedure fordetermining a braking torque that maximizes the RB current is describedbelow using symbolic closed-form expressions or solved using numericaloptimization methods.

Disclosed braking strategy is described for two different motor systemscenarios, one where an external brake is present and one where anexternal brake is absent. In the presence of an external brake, it maybe advisable to decompose the desired braking torque level into twocomponents. The electric motor applies one torque component thatprovides the maximum RB current to recover energy using the disclosed RBalgorithm, and another torque component that is provided by the externalbrake to meet the desired braking torque command from the speedcontroller (see speed controller 251′ in FIG. 2B described below).

Therefore, a braking strategy is formulated that uses this decompositionof desired torque concept, as shown in FIG. 1A which shows a torque vs.speed plot showing a desired braking torque level (calculated by thespeed controller), τ_(desired), at a desired speed, ω, that is in thenon-regenerative braking region. A non-regenerative braking region is asubset of the braking quadrants in the torque vs speed plane whereenergy from the ESS is used to provide a portion of τ_(desired).τ_(desired) can be decomposed into the optimal RB torque, τ_(regen),that provides the maximum RB current (being in the RB region) and theremaining braking torque that is applied by the external brake,τ_(ext)=τ_(desired)−τ_(regen).

For motor systems having an external brake, since the desired torquelevel is being applied by the combination of motor braking and externalmechanical braking during the braking event, this strategy does notaffect the time that it takes to slow down. In the absence of anexternal brake, disclosed RB braking strategy is designed such that ifτ_(desired) is greater than the optimal RB torque at that rotor speed,τ_(regen), then the braking torque that is applied by the motor islimited to τ_(regen) which is a function of rotor speed as describedabove. This method applies a braking torque that is less than thedesired torque level (commanded by the speed controller) therebyincreasing the time that it takes to slow the motor down. However, asignificant amount of energy is still recovered by the ESS during thebraking process.

There are a wide variety of motor applications in which braking in theshortest amount of time or the shorted distance is not required or evenneeded. In these applications, the trajectory can be planned such thatthe motor operates along the braking torque curve that produces themaximum RB current. A flow chart showing the logic for the overall RBstrategy is shown in FIG. 1B. Step 151 comprises providing a desiredbraking torque level (τ_(desired)) that is calculated by the speedcontroller. Step 152 considers whether the motor system includes anexternal brake. If the motor system includes an external brake, themethod moves to step 153 comprising having the motor controlled toprovide a torque τ_(ref)=τ_(regen), and then step 154 comprises havingthe external break controlled to provide an external brake torqueτ_(ext)=τ_(desired)−τ_(regen). If the motor system does not include anexternal break, the method moves to step 155 comprising considering canthere be a compromise to brake slowly. If there cannot there be acompromise to brake slowly, the method moves to step 156 comprisinghaving the motor controlled to provide a torque τ_(ref)=τ_(desired). Ifthere can be a compromise to brake slowly, the method moves to step 157comprising having the motor controlled to provide a torqueτ_(ref)=τ_(regen).

In order implement the disclosed braking strategy, knowledge of thebraking torque that corresponds to maximum RB current for essentiallyevery permissible speed is needed for the particular motor design. Asdescribed above, this information can be obtained from a closed-formexpression for SPMs. A closed-form expression can also be obtained forother motor types, such as switched reluctance motors, DC steppermotors, or induction motors.

Obtaining a closed-form expression for the torque that maximizes the RBcurrent is a typically a straightforward task for motors such as surfacemounted permanent magnet motors (SPMs) with the core-loss resistanceneglected. The RB controller 240 described below relative to FIG. 2B isshown using the τ_(desired) output from the speed controller shown as251′ and the angular velocity estimate {circumflex over (ω)}(n) from theEST block 215 (see FIG. 2B where it is shown as “Estimator” 215described below) to determine the level of external braking and thelevel of maximum RB current at that particular rotor mechanical speed,which is found from Equation 1 (below):

$\begin{matrix}{\tau_{regen} = {{- \left( \frac{K_{b}^{2}}{2\; R_{s}} \right)}\omega}} & (1)\end{matrix}$

where K_(b) is the back-EMF constant of the motor, R_(s) is theresistance of the stator windings, and ω is the rotor's mechanicalspeed.

As the rotor speed ω decreases, less braking torque is commanded duringoperation along the curve of maximum regenerative braking current.Therefore, the rotor speed approaches zero asymptotically and reacheszero speed in infinite time. Accordingly, there is a minimum speed,ω_(regen,min) below which the RB controller will disable operating alongthe optimal braking torque curve. The operating point is only modifiedfor points in the braking quadrants (4^(th) and 2^(nd)) that lie below(or above for the 2^(nd) quadrant) the braking torque curve thatprovides the maximum RB current.

FIG. 2A is a block diagram depiction of a controlled motor system 200without an external brake within a common FOC controller 220, accordingto an example embodiment. The motor 210 can be a permanent magnet (PM)motor or an AC (alternating current) induction motor. The FOC controller220 includes a non-volatile (NV) memory, such as a read only memory(ROM) or static random access memory (SRAM), and a processor such as acentral processing unit (CPU) that implements in software all the blocksin the encircled region shown as software as shown in FIG. 2A. Hardwarecomponents of system 200 such as implemented by a CPU and NV memory areshown in an encircled region labeled hardware to distinguish them fromcomponents of system 200 implemented in software.

System 200 includes analog circuitry 230 between the FOC controller 220and the motor 210 comprising power driver 231, 3-phase inverter 232, andsense/measurement circuits (shown as sense circuits) 233. The FOCcontroller 220 includes analog-to-digital converters (ADC's) 243 a-ccoupled to receive outputs from the sense circuits 233.

The current measurements for the respective phases Iabc output by ADC243 a is shown coupled to an input of the Clarke transform block (Clarkblock) 241 a, and the voltage measurements for the respective phasesVabc output by ADC 243 b is shown coupled to an input of the Clarkeblock 241 b, where the Clark blocks perform the known Clarketransformation which takes the measured current or voltage in the abcframe and transforms it into the α/β coordinate system to generate Iαβwhich is coupled to an input of the Park transform block (Park block)246 a, and Vαβ which is coupled to an input of the Park transform block246 b. Park blocks 246 a, 246 b also receive {circumflex over (θ)}[n].Park block 246 a, performs the known Park transformation to provideoutputs Id and Iq being measured phase current values from the statorterminals of the motor 210, and Park block 246 a performs the known Parktransformation to provide outputs Vd and Vq being measured phase voltagevalues from the stator terminals of the motor 210. Id, Iq Vd and Vq areall input to the EST block 215 labeled as “Estimator” 215.

The EST block 215 is shown outputting an angular velocity estimate{circumflex over (ω)}(n). The estimated angular velocity {circumflexover (ω)}(n) is subtracted from the reference velocity, ω_(ref), withthe result of the difference provided to the speed controller 251 asshown. The {circumflex over (θ)}[n+1] angular estimate from the ESTblock 215 is also coupled to an input of the inverse Park (iPARK) block253, which outputs Vαβ that is coupled to space-vector generator (SVgenerator) block 254, where the output of SV generator block 254 iscoupled to a PWM driver 255. The SV generator 254 computes the PWM timedurations for each phase of the motor 210 to produce the desired Vαβvoltage values. The output of the PWM driver 255 is coupled to an inputof a power driver 231 that has an output coupled to drive an input ofthe 3-phase inverter 232. In this voltage mode control embodiment, the3-phase inverter 232 forces voltage onto the stator terminals associatedwith each of the three phases of the motor 210.

The reference current generator 256 receives τ_(ref) from the speedcontroller 251 and {circumflex over (ω)}(n) from the EST 215 as inputs,and outputs I_(d,ref) and I_(q,ref) reference currents. I_(d) from thePark block 246 a is subtracted from I_(d,ref) with the result coupled toan input of a D-axis current controller 257 which provides a V_(d)output. I_(q) from Park block 246 a is subtracted from I_(q,ref) withthe result coupled to an input of a Q-axis current controller 258 whichprovides a V_(q) output. The V_(d) output and V_(q) output are bothcoupled to an iPARK block 253 which receives the V_(q) output fromQ-axis current controller 258, the V_(d) output from the D-axis currentcontroller 257, and as described above the {circumflex over (θ)}[n+1]angular estimate output by the EST block 215.

System 200 also includes a battery management circuit 260 and an ESS 265such as a battery. The battery management circuit 260 is coupled to anoutput of the inverter 232. The battery management circuit controls 260a maximum level of RB current flowing into the ESS 265 using a currentregulation circuit, wherein the maximum RB current level can be based onthe maximum charging current the ESS 265 can support.

A disclosed RB controller can be seamlessly integrated into the commonFOC system 200 shown in FIG. 2A to provide the controlled motor system(system) 250 shown in FIG. 2B having a RB controller 240 with a motorcontroller 220′ (FOC controller) for controlling a motor 210 includingan external brake 259 shown as a three-phase motor, according to anexample embodiment. In this embodiment the speed controller shown as251′ receives the difference of the reference velocity ω_(ref) and theestimated angular velocity {circumflex over (ω)}(n) from EST block 215,with this difference provided to the speed controller 251 as shown.Speed controller 251′ outputs a desired torque τ_(desired) to an inputof the RB controller 240. The RB controller 240 also receives theangular velocity estimate {circumflex over (ω)}(n) from the EST block215, and provides two outputs shown as τ_(ext) and The τ_(ref) outputfrom the RB controller 240 is shown coupled to an input of the referencecurrent generator shown as 256′ which also receives {circumflex over(ω)}(n) from EST 215 as another input, and τ_(ext) is coupled to theinput of an external brake controller 245 which is coupled to drive theexternal brake 259.

As with system 200, the reference current generator 256′ outputsI_(d,ref) and I_(q,ref) reference currents. I_(d) from the Park block246 a is subtracted from I_(d,ref) with the result coupled to an inputof a D-axis current controller 257 which provides a V_(d) output. I_(q)from Park block 246 a is subtracted from I_(q,ref) with the resultcoupled to an input of a Q-axis current controller 258 which provides aV_(q) output. The V_(d) output and V_(q) output are both coupled to aniPARK block 253 which receives the V_(q) output from Q-axis currentcontroller 258 and the V_(d) output from the D-axis current controller257. The Vαβ output of iPARK block 253 is coupled to a SV generatorblock 254, where the output of SV generator block 254 is coupled to aPWM driver 255. The SV generator 254 computes the PWM time durations foreach phase of the motor 210 to produce the desired Vαβ voltage values.The output of the PWM driver 255 is coupled to an input of the powerdriver 231 that has an output coupled to drive an input of the 3-phaseinverter 232. In this voltage mode control embodiment, the 3-phaseinverter 232 forces voltage onto the stator terminals associated witheach of the three phases of the motor 210.

The FOC controller 220 or 220′ can be a sensorless controller or can bea controller having a position sensor. FOC controllers having positionsensors can include encoders and sensors that measure position directlyand then estimate the angular speed therefrom. FOC controllers 220, 220′can be implemented by a MCU, such as the MCU chip 300 shown in FIG. 3described below. Circuitry other than a MCU can also be used to realizeFOC controller 220 or 220′, such as implementing a disclosed RBcontroller block 240, external brake controller 245 and an EST block 215using software stored in memory implemented by a computing device, andthe battery management circuit 260 using hardware/circuitry, such ascoprocessors or accelerators built using application-specific integratedcircuit (ASIC) logic gates or field programmable gate arrays (FPGAs).

FIG. 3 is a block diagram depiction of an example MCU chip 300 formed ona substrate 305 implementing the FOC controller 220′ shown in FIG. 2Bincluding the RB controller 240, external brake controller 245, andbattery management circuit 260, according to an example embodiment.Although not shown, the MCU chip 300 typically includes other integratedcircuit modules, for example, a Universal Serial Bus (USB) controllerand a transceiver. MCU chip 300 is shown including NV memory 272,volatile data memory 273 shown as “data memory volatile”, digital I/O(interface) 274, central processing unit (CPU) 275, and clock (or timer)276. Core for implementing the EST block 215, RB controller 240,external brake controller 245 are shown collectively as 282 stored in NVmemory 272, although it is possible one or more of these blocks or thecontroller can be implemented in hardware. MCU chip 300 is also shownincluding a digital data bus 278 and an address bus 279.

MCU chip 300 is shown as a monolithic integrated circuit (IC). Thesubstrate 305 may comprise silicon, such as bulk silicon or silicon epion a bulk silicon substrate. The substrate 305 may also generallycomprise other materials, such as elementary semiconductors besidessilicon including germanium. Substrate 305 may also comprise a compoundsemiconductor.

FIG. 4 shows steps in an example method 400 of RB where each torque vs.speed value generated is designed to maximize the RB current returned tothe ESS, according to an example embodiment. Step 401 comprisesproviding an electric motor (motor) comprising at least one statorhaving a winding with a stator terminal, and a rotor, a measured orestimated speed of the rotor (rotor speed), a motor controller thatregulates a current level in the winding, and a power inverter whichcontrols an energy flow to the stator terminal. An ESS is also providedwhich exchanges energy with the motor, a battery management circuit iscoupled between the ESS and the power inverter, and a processor has anassociated memory storing a RB algorithm, where the processor isprogrammed to implement the RB algorithm during braking to cause themotor controller to execute steps 402 and 403.

Step 402 comprises determining a value for RB torque (RB torque value)from the rotor speed that maximizes a level of RB current (maximum RBcurrent). Step 403 comprises using the power inverter to redirect themaximum RB current to maximize a power transfer from the motor to theESS.

The battery management circuit can control the maximum RB currentflowing into the ESS using a current regulation circuit based on amaximum charging current level supported by the ESS. In some embodimentsthe motor includes an external brake, where the method further comprisesdetermining a value for an external braking torque from the rotor speedto provide additional mechanical braking, and decomposing a desiredtorque level into two components wherein the motor controller appliesthe RB torque value as one torque component to provide the maximum RBcurrent to recover energy and a second torque component is provided bythe external brake to the motor to meet the desired torque command fromthe speed controller.

Benefits of disclosed algorithms include disclosed RB algorithms can beimplemented for a variety of motor controllers, for example for theTexas Instruments' INSTASPIN-FOC sensorless motor control technology,such as for PICCOLO and POTENZA MCU chip-based motor controllers. In thecase of INSTASPIN-FOC technology and related technology, code for thedisclosed RB algorithms can be embedded in the ROM of the MCU chip (seeNV memory 272 in FIG. 3).

Uses for disclosed embodiments include for electric automobiles such asthe Tesla Model S P85+. Other example applications include any systemthat uses electric motors that operate at times with slowing orstopping, such as manufacturing and assembly lines, white appliances,elevators, cranes, and quadcopters.

Any equation described herein may be implemented by either hardware orby software. Regarding hardware-based implementations, a disclosedequation can be converted to a logic gate pattern, such as using VHDLwhich can then be realized such as using FPGA or application-specificintegrated circuit (ASIC) to implement the logic gate pattern. VHDL isan acronym which stands for VHSIC (Very High Speed Integrated Circuits)Hardware Description Language. For example, a software-basedimplementation can be realized using a math library provided by aconventional MCU chip.

Examples

Disclosed embodiments are further illustrated by the following specificExamples, which should not be construed as limiting the scope or contentof this Disclosure in any way.

Simulation Results

The disclosed RB algorithm was applied to a battery poweredconverter-controlled electric machine. The electric machine model wasthe Anaheim Automation Brushless DC motor (P/N: BLY172S-24V-4000). Thebattery pack comprised six A123 Racing AR26650M1B Li-Ion Nano Cells witheach cell having a nominal voltage of 3.3V. The battery pack had anominal voltage of 19.8V and an internal resistance of 36 mOhm. Theparameters of the system are listed in Table 1 below.

TABLE 1 Parameters of the motor system used for Simulations ParameterDescription Value Units E_(s) Nominal Open Circuit Battery Voltage 19.8V R_(s) Internal Resistance of Battery 0.036 Ohms N Number of Pole-Pairsof PMSM 4 — R_(p) Per-Phase Stator Winding Resistance of PMSM 1.2 OhmsR_(c) Per-Phase Core Loss Resistance of PMSM 150 Ohms L_(d) D-axisInductance of PMSM 1.8 mH L_(q) Q-axis Inductance of PMSM 1.8 mH ΛMagnitude of Permanent Magnet Flux 0.010998 V/rad/s I_(max) MaximumLength of Current Vector in the d-q plane 5.091 A max (U_(dq)) MaximumAssignable Length of the Duty-Cycle Vector in the d-q plane$\frac{3}{2\sqrt{2}}$ — ω_(max) Maximum Mechanical Speed of the Machine9000 RPM J_(m) Rotor Inertia 4.8 × 10⁻⁶ Kg-m² β_(m) Rotor ViscousFriction Co-efficient 5.0 × 10⁻⁶ Nm/rad/s

The motor system was loaded with an external inertia and viscousfriction load for the simulations. The system was assumed to start froma non-zero equilibrium point (non-zero speed and currents) and wasslowed down to zero speed using closed-loop speed control with RBdisabled (as a control) and enabled. The performance metrics aremeasured in terms of stopping time and energy recovered at the terminalsof the battery. The energy recovered at the terminals of the battery isthe time integral of the product of DC bus current and DC bus voltaget=0 to t=t_(stop).

E _(elec)=∫_(t=0) ^(t) ^(stop) i _(dc) v _(dc) dt

If the value of E_(elec) is negative, then it means that energy wasreturned to the ESS (regenerative braking) during the braking event andif the value of E_(elec) is positive, then energy was removed from theESS (non-regenerative braking) during the braking event. If the initialspeed of the combined rotor-load combination is ω₀, then the initialkinetic energy stored in the rotor is:

E _(mech,init)=½(J _(m) +J _(L))ω₀ ²

The ratio if energy is recovered is expressed as:

$E_{ratio} = \left\{ \begin{matrix}{- \frac{E_{elec}}{E_{{mech},{init}}}} & {,{{{if}\mspace{14mu} E_{elec}} < 0}} \\0 & {,{otherwise}}\end{matrix} \right.$

The value for ω_(regen,min) was set to zero for the simulations. Thevalue of rotor speed was initially set to ω₀=100 rad/s. The value of theinitial kinetic energy stored in the rotor-load combination was 1013.6mJ. The results of the simulation for the scenario with regenerativebraking disabled and enabled are shown in Table 2 below. The speedcontroller gains are not changed between the RB disabled and enabledcases.

TABLE 2 Simulation Results with Regenerative Braking Disabled andEnabled Viscous Regenerative Braking Regenerative Braking FrictionDisabled Enabled Load Co-efficient, Electric Electric Inertia, J_(L)β_(L) Stopping Energy, Stopping Energy, (kg-m²) (Nm/rad/s) Time (ms)E_(elec) (mJ) Time (ms) E_(elec) (mJ) 1.98 × 3.16 × 203.7 550.51 1193.9−432.4 10⁻⁴ 10⁻⁵

It can be seen that operation with the RB algorithm disabled stops veryfast but consumes energy from the battery to do so (E_(ratio)=0). Incontrast, operation with the RB algorithm enabled has recovered about42.65% of the initial kinetic energy (E_(ratio)=0.4265), however it tookabout six times longer to come to a stop.

The simulation plots for the scenarios in Table 2 are described below.The speed response for the case with the RB algorithm disabled is shownin FIG. 5. The braking trajectory in the torque-speed plane is shown inFIG. 6. It can be seen that most of the braking trajectory is in thenon-RB region (below the maximum regenerative braking boundary) whichexplains why there was no charge returned to the battery.

FIG. 7 shows simulation results for scenario with the RB algorithmenabled. The speed response as seen in FIG. 7 approaches zeroasymptotically. A faster braking event can be achieved by setting thevalue of ω_(regen,min) to a non-zero value at the cost of less energybeing recovered by the RB algorithm. The braking trajectory as seen inFIG. 8 approaches and stays on the curve of maximum regenerative brakingcurrent defined by equation 1 shown above. This results in maximumcurrent flowing back into the battery at every rotor speed.

The motor system described in Table 1 above was set up on the laboratorybench with an aluminum disc as the inertial load. The machine wascontrolled using the Multi-Axis Motor Control Kit with the TMS320F28069Piccolo series microcontroller from Texas Instruments. The values ofinertial load and viscous friction co-efficient correspond to those ofcase 4 of Table 2. The inertial load was accelerated to a constant speedof 100 rad/s and then brought to a stop with the RB algorithm disabledand enabled. The results of the experiment are shown in Table 3 belowand the measured speed responses for the RB algorithm disabled andenabled are shown in FIG. 9 and FIG. 10, respectively.

The experimental results show that the stopping time with the RBalgorithm enabled is about 3.5 times that with the RB algorithmdisabled. With the RB algorithm disabled, the battery expends energy inorder to bring the inertia to a stop resulting in a net positiveelectric energy as seen in Table 3. However with the RB algorithmenabled, there is a conversion of mechanical energy from the rotatinginertial load to electrical energy that charges the battery. The energyrecovered in the case with the RB algorithm enabled was about 41.38% ofthe initial kinetic energy that was stored in the rotating rotor-loadcombination. When comparing the simulation results to the experimentalresults, the stop time in the experiments is shorter than thesimulations. The primary reason for this difference is due to unmodeleddynamics in the system simulation such as inverter loss. This unmodeledeffect is also visible in the amount of energy stored back into thebattery, which is less for the experiments than for the simulations.

TABLE 3 Experimental Results with Regenerative Braking Disabled andEnabled Viscous Regenerative Braking Regenerative Braking FrictionDisabled Enabled Load Co-efficient, Electric Electric Inertia, J_(L)β_(L) Stopping Energy, Stopping Energy, (kg-m²) (Nm/rad/s) Time (ms)E_(elec) (mJ) Time (ms) E_(elec) (mJ) 1.98 × 3.16 × 192.0 427.2 712.0−419.5 10⁻⁴ 10⁻⁵

CONCLUSION

From the simulations and experiments, it can be concluded that by usinga disclosed RB algorithm there is a significant increase in chargingpower going into the ESS such as a battery at the expense of an increasein average stopping time for a motor system with no external mechanicalbrake. However, as described above, disclosed embodiments can alsobenefit motor systems having an external mechanical brake.

Those skilled in the art to which this disclosure relates willappreciate that many other embodiments and variations of embodiments arepossible within the scope of the claimed invention, and furtheradditions, deletions, substitutions and modifications may be made to thedescribed embodiments without departing from the scope of thisdisclosure.

1. A non-transitory computer-readable medium storing instructions thatwhen executed on a computing system causes the computing system to:determine a value for regenerative braking torque (RB torque value) froma rotor speed of an electric motor that maximizes a level of a RBcurrent (maximum RB current), and use a power inverter to redirect themaximum RB current to maximize a power transfer from the electric motorto an energy storage system (ESS).
 2. The method of claim 1, wherein abattery management circuit controls the maximum RB current using acurrent regulation circuit based on a maximum charging current levelsupported by the ESS.
 3. The method of claim 1, wherein the electricmotor includes an external brake, further comprising: determining avalue for an external braking torque (τ_(ext)) from the rotor speed toprovide additional mechanical braking, and decomposing a desired brakingtorque level (τ_(desired)) determined by a speed controller into twocomponents wherein a motor controller applies said RB torque value asone torque component to provide said RB current and a second torquecomponent provided by said external brake to said motor to meet saidτ_(ext).
 4. The method of claim 1, wherein the electric motor comprisesa permanent magnet (PM) motor.
 5. The method of claim 1, wherein theelectric motor comprises an alternating current (AC) induction motor. 6.The method of claim 4, further comprising computing the RB torque value(τ_(regen)) using:$\tau_{regen} = {{- \left( \frac{K_{b}^{2}}{2\; R_{s}} \right)}\omega}$wherein the ω is the rotor speed, the K_(b) is a back-EMF constant ofthe PM motor, and the R_(s) is a resistance of the stator.
 7. The methodof claim 1, wherein the electric motor comprises an interior permanentmagnet (IPM), further comprising offline computing a plurality of the RBtorque values versus the rotor speed and compiling a table therefrom,and using the table for the determining the RB torque value inreal-time.
 8. The method of claim 1, wherein the RB algorithm utilizes aclosed-form expression that relates the RB torque values with themaximum RB current for a given value of the rotor speed.
 9. The methodof claim 1, wherein the motor controller implements field-orientedcontrol (FOC).